You do not need an online account to use the Zotero desktop app. However, having an online account allows you to sync your sources and then gives you access to them even if you aren't using your computer. Also, if you plan to use the Group/Sharing feature, an online account is required.
Creating an Account
- Go to the Zotero.org
- Click the Log In link in the upper right hand corner of the page
- Click the Register link in the upper right hand corner of the next page
- Complete the required fields, check the 'I am not a robot' box, and click Register
- Once your account is created, you can sync your desktop sources to your online account